Destructive and nondestructive evaluations of the effect of moisture absorption on the mechanical...

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Destructive and nondestructive evaluations of the effect of moisture absorption on the mechanical properties of polyester-based composites Roman Šturm a , Raimond Grimberg b,1 , Adriana Savin b , Janez Grum a,a University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, Slovenia b Nondestructive Testing Department, National Institute of R&D for Technical Physics, Iasi, Romania article info Article history: Received 31 March 2014 Received in revised form 3 October 2014 Accepted 17 November 2014 Available online 22 November 2014 Keywords: A. Polymer-matrix composites (PMCs) B. Mechanical properties B. Wettability D. Non-destructive testing abstract In this study the effect of moisture absorption on the mechanical properties of glass-reinforced polyester composites is evaluated using both destructive and nondestructive tests. The composite resins were pro- duced with two different production processes, while the mechanical properties of the composite mate- rials were measured using DMA destruction tests. According to the DMA tests, the dependency in terms of temperature for the real component of the complex elastic modulus (E 0 ), the imaginary component of the complex elastic modulus (E 00 ), as well as tan(d) can be traced. For a more efficient use of the composite materials, the compliance tensor was obtained with nondestructive tests based on ultrasound. A method for the generation and reception of Lamb waves in plates of composite materials is described, based on using air-coupling, low-frequency, ultrasound transducers in a pitch–catch configuration. The results of the nondestructive measurements made in this study are in good agreement with those obtained when using the DMA destructive tests. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction The mechanical properties of a material determine its manufac- turability, performance, and longevity. This means that a knowl- edge of the mechanical properties is essential for making good design decisions. Polymers are exceptionally complex materials – their mechanical properties depend on chemistry, processing, and the thermo-mechanical history, as well as on volume con- straints. Thus, in order to gain useful information for making sound decisions when designing with polymer composites, mechanical property measurements should be made on a relevant sample in a relevant context [1–7]. Glass-fiber-reinforced polyester (GFRP) is the most ‘‘popular’’ composite, with a matrix based on cured, thermosetting resin. Its first main civilian application was for boat building. Other uses of GFRPs include hot tubs, pipes for drinking water and sewers, office plant-display containers and flat-roof sys- tems. Mayer [1] showed that the mechanical performance of GFRP composites depends on the fibers’ strength and modulus, the strength of the matrix and the chemical stability. In addition to this, Erden et al. [2] showed that matrix modifications can enhance the mechanical properties of glass-polyester composites. Rowell [3] demonstrated fiber-reinforced composite materials that offer a combination of strength and modulus that are either comparable to, or better than, many pure materials. But thermoplastics exhibit a hydrophobic nature, as was demonstrated by Kim et al. [8]. When glass–polyester composites are immersed in water, uptake of the water can occur. This is the result of the capillarity of the materials and the water absorption of the hydrophilic groups in the glass fiber and the unsaturated polyester. Huang and Sun [9] and Visco et al. [10] concluded that a reaction between the water molecules and the matrix could deteriorate the interface, resulting in a weaker material. Kouba et al. showed a simple modelling of impregnation in pultrusion process of thermoplastic composites [11]. The performance of GFRP pipes is critical in many engineering applications when they are subjected to a combination of high- temperature/high-humidity environments. The diffusion of water or an aqueous fluid into GFRP pipes may lead to changes in the thermo-physical, mechanical, and chemical characteristics. Many of these changes can result in a degradation of the material’s per- formance. In order to properly predict the service life of a GFRP pipe, we need to understand the mechanisms that govern these changes. Water absorption by the resin may cause both reversible and irreversible changes to the resin, including hydrolysis, plasticiza- tion, micro-cracking, and even the glass-transition temperature [12–15]. For a reversible process, the mechanical properties can usually be recovered by drying; however, for the irreversible case, http://dx.doi.org/10.1016/j.compositesb.2014.11.022 1359-8368/Ó 2014 Elsevier Ltd. All rights reserved. Corresponding author. 1 Deceased. Composites: Part B 71 (2015) 10–16 Contents lists available at ScienceDirect Composites: Part B journal homepage: www.elsevier.com/locate/compositesb

Transcript of Destructive and nondestructive evaluations of the effect of moisture absorption on the mechanical...

Composites: Part B 71 (2015) 10–16

Contents lists available at ScienceDirect

Composites: Part B

journal homepage: www.elsevier .com/locate /composi tesb

Destructive and nondestructive evaluations of the effect of moistureabsorption on the mechanical properties of polyester-based composites

http://dx.doi.org/10.1016/j.compositesb.2014.11.0221359-8368/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.1 Deceased.

Roman Šturm a, Raimond Grimberg b,1, Adriana Savin b, Janez Grum a,⇑a University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, Sloveniab Nondestructive Testing Department, National Institute of R&D for Technical Physics, Iasi, Romania

a r t i c l e i n f o

Article history:Received 31 March 2014Received in revised form 3 October 2014Accepted 17 November 2014Available online 22 November 2014

Keywords:A. Polymer-matrix composites (PMCs)B. Mechanical propertiesB. WettabilityD. Non-destructive testing

a b s t r a c t

In this study the effect of moisture absorption on the mechanical properties of glass-reinforced polyestercomposites is evaluated using both destructive and nondestructive tests. The composite resins were pro-duced with two different production processes, while the mechanical properties of the composite mate-rials were measured using DMA destruction tests. According to the DMA tests, the dependency in termsof temperature for the real component of the complex elastic modulus (E0), the imaginary component ofthe complex elastic modulus (E00), as well as tan(d) can be traced. For a more efficient use of the compositematerials, the compliance tensor was obtained with nondestructive tests based on ultrasound. A methodfor the generation and reception of Lamb waves in plates of composite materials is described, based onusing air-coupling, low-frequency, ultrasound transducers in a pitch–catch configuration. The results ofthe nondestructive measurements made in this study are in good agreement with those obtained whenusing the DMA destructive tests.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The mechanical properties of a material determine its manufac-turability, performance, and longevity. This means that a knowl-edge of the mechanical properties is essential for making gooddesign decisions. Polymers are exceptionally complex materials –their mechanical properties depend on chemistry, processing,and the thermo-mechanical history, as well as on volume con-straints. Thus, in order to gain useful information for making sounddecisions when designing with polymer composites, mechanicalproperty measurements should be made on a relevant sample ina relevant context [1–7]. Glass-fiber-reinforced polyester (GFRP)is the most ‘‘popular’’ composite, with a matrix based on cured,thermosetting resin. Its first main civilian application was for boatbuilding. Other uses of GFRPs include hot tubs, pipes for drinkingwater and sewers, office plant-display containers and flat-roof sys-tems. Mayer [1] showed that the mechanical performance of GFRPcomposites depends on the fibers’ strength and modulus, thestrength of the matrix and the chemical stability. In addition tothis, Erden et al. [2] showed that matrix modifications can enhancethe mechanical properties of glass-polyester composites. Rowell[3] demonstrated fiber-reinforced composite materials that offer

a combination of strength and modulus that are either comparableto, or better than, many pure materials. But thermoplastics exhibita hydrophobic nature, as was demonstrated by Kim et al. [8]. Whenglass–polyester composites are immersed in water, uptake of thewater can occur. This is the result of the capillarity of the materialsand the water absorption of the hydrophilic groups in the glassfiber and the unsaturated polyester. Huang and Sun [9] and Viscoet al. [10] concluded that a reaction between the water moleculesand the matrix could deteriorate the interface, resulting in aweaker material. Kouba et al. showed a simple modelling ofimpregnation in pultrusion process of thermoplastic composites[11].

The performance of GFRP pipes is critical in many engineeringapplications when they are subjected to a combination of high-temperature/high-humidity environments. The diffusion of wateror an aqueous fluid into GFRP pipes may lead to changes in thethermo-physical, mechanical, and chemical characteristics. Manyof these changes can result in a degradation of the material’s per-formance. In order to properly predict the service life of a GFRPpipe, we need to understand the mechanisms that govern thesechanges.

Water absorption by the resin may cause both reversible andirreversible changes to the resin, including hydrolysis, plasticiza-tion, micro-cracking, and even the glass-transition temperature[12–15]. For a reversible process, the mechanical properties canusually be recovered by drying; however, for the irreversible case,

R. Šturm et al. / Composites: Part B 71 (2015) 10–16 11

the mechanical properties are permanently altered. Deniz et al.[16] described the effect of seawater on failure pressure and itsimpact on the behaviors of polymer–matrix composites.

Huang [17] used a common method to evaluate the failurebehavior of materials with a dynamic mechanical analysis(DMA). Many studies have shown that temperature and the envi-ronment are the most critical factors in reducing the strength ofGFRP materials. Ray [18] has demonstrated that the higher thetemperature of the environment and the longer is the exposuretime, the larger will be the decrease in the strength and modulusof the GFRP. In those applications in which GFRP composites aresubject to heat and a mechanical load, it is essential to determinatethe elastic properties using nondestructive methods. A non-destructive evaluation offers advantages compared to conventionalpolymer-characterization methods, and without extracting testspecimens. Schmerr [19], Krautkramer and Krautkramer [20] andRojek et al. [21] found that the best methods for elastic-propertiesdeterminations are the ultrasound methods. El-Sabbagh et al. [22]studied the feasibility of using an ultrasonic longitudinal soundwave in the definition of the fiber content and the distribution innatural fiber composites.

Grimberg et al. [23] proposed the use of measuring of propaga-tion speed of longitudinal and transversal waves, as well as Lambwaves for characterization overheated zones in fiber reinforcedplastics composites. Santos et al. [24] have used guided waves(Lamb waves) to characterize the effect of multiple impacts in lam-inate composites. The analysis of the impact has been made by twoparameters; amplitude response and time shift. PZT sensors havebeen bonded to the samples in a pitch-and-catch configurationand the Lamb wave symmetrical mode (S0) signal was used. Fahimet al. [25] have designed and developed a non-destructive monitor-ing technique based on ultrasonic transmission through thickness.A sensible analysis has shown that the Young modulus can be rea-sonably well identified.

2. Experimental procedure

2.1. Sample preparation

Samples of GFRP plates having as their reinforcement six sheetsof ravings with 250 ± 50 gm�2 density and a matrix made from dif-ferent types of unsaturated Orthophthalic polyester resins, madeby Helios, Slovenia, were used in this study. The characteristicsof the studied GFRP samples are presented in Table 1.

2.2. Water-absorption test

The effect of water absorption on the GFRP composites wasinvestigated. Initially, DMA measurements on non-immersed sam-ples and immersed samples were conducted on unconditionedsamples. The obtained results were inconclusive. For this reason,the measurements were remade, this time on conditioned samples,i.e., with the water that might be in the initial samples beingeliminated.

The conditioning involved maintaining all the samples in a dry-ing oven at 50 �C for 5 days. For each type of composite, one samplewas weighed in order to record the initial mass. This sample was

Table 1Studied GFRP samples.

Sample name Matrix Fiber volume ratio Den

7201 COLPOLY 7201 0.43 ± 0.005 1557524 COLPOLY 7524 0.43 ± 0.005 1537243 COLPOLY 7243 0.57 ± 0.005 141

marked. The immersion was carried out in distilled water andthe immersion periods were 3, 6, 9, 12, 20, 40 and 100 days. As aresult of a mistake, the sample from the 7524 composite immersedfor 100 days is missing from the results.

After each period of immersion, two examples of each type ofsample were removed, one of samples was used for the determina-tion of the adsorbed water and the second one was used for theDMA measurements. The adsorbed water was determined fromweighing samples after each period.

Mtð%Þ ¼Mt �M0

M0� 100 ð1Þ

where M0 is the mass of the non-immersed sample after the condi-tioning and Mt is the mass of the same sample immersed for time t.Fig. 1 presents the dependency of Mt(%) on the immersion time forthe three types of composites used in the study.

As reviewed by Weitsman [26], the water-absorption behaviorof composite materials can be categorized into several types. Ithas been argued that under most conditions the moisture contentof composites may be calculated using Fick’s law [27]. Experimen-tal evidence indicates that for most types of polymeric compositematerials the hydrothermal behavior is Fickian in nature. Theabsorption and desorption curves when plotted against time arealways concave towards the time axis and asymptotically reachthe equilibrium value [28]. We can also find a new diffusion modelthat extends the classical Fickian theory to include the effects ofthe interaction of diffusing molecules with the chemical and phys-ical structure of polymeric composites [29]. The curves in Fig. 1denote linear Fickian behavior, where the moisture-related weightgain gradually attains equilibrium after a rapid initial take off.

In order to determine the water-diffusion coefficient in a com-posite, the data from Fig. 1 were converted so that the abscissa ofthe graphic in Fig. 2 is in the form of

ffiffitp

expressed inffiffiffiffiffiffiffisecp

.It is assumed that the studied composites absorb the water in

accordance with the law of Fick, as shown in Shen et al. [30]:

Mt

M1¼ 4

h

ffiffiffiffiffiffiDtp

rð2Þ

where M1 represents the maximum quantity of water that diffusesinto the composite and h is the thickness of the sample. The valuesfor the diffusion coefficients are given in Table 2.

3. Results and discussion

3.1. DMA measurements

The measurements of the elastic modulus along the three direc-tions were made with a Dynamic Mechanical Analyzer DMA 242Cfrom Netzsch, Germany with a three-point bending fixture andusing the analysis software Proteus v.4.8.5. The measurementswere carried out at a frequency of 1 Hz.

Polymers are often employed in products because of their abil-ity to both store and damp energy. The complex modulus E⁄ is aphase vector that incorporates both capacities:

E� ¼ E0 þ jE00 ð3Þ

where j ¼ffiffiffiffiffiffiffi�1p

.

sity (kg/m3) Observations Production process

0 ± 20 Medium reactivity resin In two steps0 ± 20 Chemical resistance In situ0 ± 20 Preaccelerated thixotropic In two steps

Fig. 1. Water uptake vs. immersion time.

Fig. 2. Water uptake vs.ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiimmersiontimep

inffiffisp

.

Table 2Diffusion coefficient of moisture in different composites.

Composite D (m2s�1)

7201 1.81 � 10�12

7524 1.5355 � 10�12

7543 9.55 � 10�13

Fig. 3. The temperature dependence of the storage modulus E0 .

12 R. Šturm et al. / Composites: Part B 71 (2015) 10–16

The real part (E0) of the complex modulus is called the storagemodulus because it quantifies the material’s ability to store energyelastically. In materials with insignificant damping, the storagemodulus is equivalent to the Young’s modulus. The imaginary partof the complex modulus (E00) is called the loss modulus, because itquantifies the material’s ability to dampen out the energy. Thedimensionless loss factor tan(d) is independent of the contactenergy, because it is the ratio of the loss to the storage modulus:

tanðdÞ ¼ E00

E0ð4Þ

The mechanical performance of a composite material dependsstrongly on its glass-transition temperature, Tg. Above this temper-ature the mechanical properties decrease rapidly. Therefore, it isnecessary to check the influence of the moisture on the glass-transition temperature of the GFRP specimen. The glass-transitiontemperature of the samples was determined with a DMA instru-ment. Both dry and immersed specimens were tested to determinethe aging produced by water immersion. Figs. 3–5 present the

DMA results for dry and wet GFRP specimens. The storage modu-lus, the loss modulus, and the loss factor are taken as the ordinate,while the temperature is taken as the abscissa. Some observationswere made. First, there are some changes with respect to the stor-age modulus, the loss modulus, and the loss factor, i.e., the peakvalue of the loss factor. At relatively low temperatures (0–40 �C)the polymer is stiff and has a high storage modulus E0 and a lowmodulus E00. The chains are frozen in fixed positions because insuf-ficient energy for the translational and rotational motions of thepolymer segments is available. As the temperature increases, thepolymer obtains sufficient thermal energy to enable its chains tomove more freely. At temperatures higher than 100 �C the storagemodulus decreases to about 500 MPa. The increase in E0 after3 days of immersion is due to the fact that the water acts as plas-ticizer, initially, and then, once with the increasing of the immer-sion time, E0 decreases (Fig. 3). In analogy with this process atransition occurs at temperatures between 60 and 100 �C, andthe loss modulus E00 goes through a maximum. This region isreferred to as the glass–rubber transition or glass transition Tg

and can be qualitatively interpreted as the onset of large-scale con-formational rearrangements of the polymer chain’s backbone. Thetemperature at which this peak maximum is observed is conven-tionally defined as Tg.

Fig. 5 shows the loss factor tan(d) of both dry and wet speci-mens. The peak value of tan(d) is considered as the glass-transitiontemperature. For each immersion time and each composite, theglass-transition temperature Tg and the activation energy for theglass transition Eg as the basis of the Arrhenius rule were deter-mined. One can see clearly that moisture absorption by thespecimen results in a change of Tg, which indicates a degradationprocess in the material (Fig. 6). It can also be seen that the wateracts initially as a plasticizer.

However, after 100 days of immersion in water, the glass-transition temperature is almost the same as it is for the non-immersed specimens (Fig. 6). Fig. 7 also presents the glass-transition activation energy vs. the immersion time for all threecomposites.

3.2. The principle of the ultrasound-measurement method

In order to measure the propagation speed of the ultrasoundlongitudinal and transversal waves we used a Pulser Receiver5073 PR Panametrics NDT, USA, in impulse–echo mode, with thesignal received being visualized on Digital Oscilloscope LeCroyWaveRunner 64Xi with a 600-MHz passband and a 10 GS/s sam-pling rate. A transducer G5KB–GE USA was used for the generationof the longitudinal waves with ZG-F gel Krautkramer, Germany forthe coupling and MB4Y-GE, USA for the transversal waves usinghoneybee wax as the coupling. The transducers were placed on adelay block made from Plexiglas with a thickness of 20 mm.

Fig. 4. The temperature dependence of the loss modulus E00 .

Fig. 5. The temperature dependence of the loss factor tan(d).

Fig. 6. Glass-transition temperature vs. immersion time.

Fig. 7. Glass-transition activation energy vs. immersion time.

R. Šturm et al. / Composites: Part B 71 (2015) 10–16 13

The principle scheme of the equipment is presented in Fig. 8a,and the physical realization is presented in Fig. 8b.

The measurements for the phase velocity of the Lamb waves,modes A0 and S0 were made using air-coupling US transducers,pitch-catch configuration, NCG100S25–UltranGroup, USA, havinga central frequency of 100 kHz. The critical incident angle was cal-culated according to Eq. (5), considering cair = 340 m/s and cs hav-ing the value obtained by a determination of the transversalwaves-propagation speed. The value of hcritic was 10.2�.

h ¼ arcsincair

csz

� �ð5Þ

The incident angle, h, is chosen so h > hcritic.The determination of the phase velocity of the fundamental

modes S0 and A0 was made using the phase-spectrum method

demonstrated by Sachse and Poo [31]. The phase velocity of theLamb waves is given by:

cp ¼2pfLDu

ð6Þ

where Du is the difference in the phase spectrum of two signalsthat were collected with a different distance between them of L,and f is the frequency.

For a simpler visualization of the modes and to determine thegroup velocity of the Lamb wave we can use the method of a‘‘spectrogram’’, presented by Boashash [32], which represents atime-varying spectral representation that shows how the spectraldensity of a signal delivered by the US reception transducer varieswith time.

The studied GFRP samples are all transversally isotropic, as wasexperimentally demonstrated. An elastic medium is transversallyisotropic if the elastic characteristics remain invariant for all pointsin directions symmetrical with respect to an axis. Accordingly, if Zis the axis of transverse isotropy, then the material is ‘‘isotropic’’ inthe planes normal to the Z axis.

In the case of transverse isotropy, only five elastic coefficientscan be independent, as shown by Lamaitre and Chaboche [33].Balasubramaniam et al. [34] have used ultrasonic non-destructivetesting methods to determine the five independent elastic proper-ties as well as the corresponding engineering constants of compos-ite specimens. More precisely, the isotropy normal to the Zdirection (Fig. 9) requirement requires that

e ¼ A � r ð7Þ

or

ex

ey

ez

exy

eyz

exz

8>>>>>>>><>>>>>>>>:

9>>>>>>>>=>>>>>>>>;¼

1Ex

� txy

Ex� txz

Ex0 0 0

� txy

Ex

1Ex

� txzEx

0 0 0

� txzEx� txz

Ex

1Ez

0 0 0

0 0 0 1þtxy

Ex0 0

0 0 0 0 12Gxz

0

0 0 0 0 0 12Gxz

266666666664

377777777775�

rx

ry

rz

rxy

ryz

rxz

8>>>>>>>><>>>>>>>>:

9>>>>>>>>=>>>>>>>>;

ð8Þ

where e is the strain vector, r is the stress vector, and A representsthe tensor of elastic compliance.

In addition, we have the following equalities:

Ex = Ey – extensional moduli coefficients in the directions X andY;txz/Ex = tyz/Ey – contraction coefficients in the directions X andY, for a tension applied in the direction Z;

Fig. 8. The experimental set-up for the determination of the Lamb wavespropagation speed using an air-coupled US transducer: (a) basic scheme; (b)photograph.

Fig. 9. The coordinate system attached to the GFRP plate.

Table 3Mechanical properties determined by DMA.

Composite Ex = Ey

(GPa)Ez

(GPa)txy Tg

(�C)Activation energy (kJ/mol)

7201 9.1 8.2 0.2 82.9 149.67524 10.5 9.65 0.2 110.7 286.27243 8.4 8.2 0.2 105.7 296.4

Fig. 10. The experimental results: (a) The signal received by the receptiontransducer during the examination of the 7201 composite; (b) the amplitudespectrum; (c) the spectrogram.

14 R. Šturm et al. / Composites: Part B 71 (2015) 10–16

Gxz = Gyz – shear moduli for shear in the planes perpendicular tothe axis Y and the axis Z;

The five coefficients that characterize the material are– Two Young’s (or extensional) moduli Ex and Ez.– Two shear moduli Gxz.– Two Poisson’s ratios txz and tyz.

Krautkramer and Krautkramer [20] showed that the Young’smodulus Ez, the shear modulus Gxz and the Poisson’s ratio txz canbe determined by measuring the velocities of the longitudinalwaves cpz

and of the transversal waves csz that propagate alongthe Z direction:

cpz¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEzð1� txzÞ

qð1þ txzÞð1� 2txzÞ

s

csz ¼

ffiffiffiffiffiffiffiGxz

q

sð9Þ

According to Lemaitre and Chaboche [33], Eq. (9) can beexpressed as a function using the Lamé coefficients k and l, takinginto account the basic relationship:

kz ¼Eztxz

ð1þ txzÞð1� 2txzÞ

Table 4Mechanical properties evaluated with ultrasound measurements.

Composite Cp (ms�1) Cs (ms�1) CA0 (ms�1) CS0 (ms�1) Ex = Ey (GPa) Ez (GPa) txy txz Gxy (GPa) Gxz (GPa)

7201 2261 1550 912 1980 8.9 7.9 0.2 0.19 3.7 3.67524 2844 1603 1094 2230 10 9.5 0.2 0.27 4.2 3.07243 2868 1512 1036 2250 8.3 8.4 0.21 0.31 4.2 3.2

R. Šturm et al. / Composites: Part B 71 (2015) 10–16 15

lz ¼ Gxz ð10Þ

To determine the Young’s modulus Ex and the Poisson’s ratio txy,the expression of the phase velocities of the fundamental modes ofLamb’s wave propagation can be used.

Schmerr [19] has shown that the phase velocity of the Lambwaves satisfies the dispersion equation:

tanhðbhÞtanhðahÞ ¼

4k2ab

ðk2 þ b2Þ2

" #�1

ð11Þ

where the sign ‘‘ + ’’ from the exponent corresponds to the symmet-ric (extensional) modes and the sign ‘‘�’’ corresponds to the anti-symmetric (flexural) modes.

a2 ¼ k2 � k2px

b2 ¼ k2 � k2sx

ð12Þ

where k ¼ x=cphrepresents the wave number for the phase velocity

of the Lamb wave; kpx¼ x=cpx

is the wave number for the longitu-dinal waves that propagate in the X direction; ksx ¼ x=csx is thewave number for the transversal waves that propagate in the Xdirection; and 2h is the plate thickness (Fig. 9).

Generally, the solution of Eq. (11) is rather complex, and it mustbe found numerically. However, some special cases can be treatedanalytically. At low frequencies, the hyperbolic tangent term in Eq.(11) can be approximated as

tanhðahÞ ffi ah

tanhðbhÞ ffi bh

For the symmetrical modes at low frequencies, Eq. (11)becomes

ðk2 þ b2Þ ¼ 4k2a2 ð13Þ

Lemaitre and Chaboche [33], Schmerr [19], and Grum et al. [35]have shown that according to a basic relationship, we can expressfor the fundamental symmetrical mode, S0, the phase speed as:

cS0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Ex

qð1� t2xyÞ

sð14Þ

The phase speed for the fundamental anti-symmetrical mode,A0, can be obtained after a few algebraic calculations:

cA0 ¼Dp

2qh

� �1=4

x1=2 ð15Þ

where Dp is the flexural rigidity of the plate:

Dp ¼8lxðkx þ lxÞh

3

3ðkx þ 2lxÞð16Þ

and kxand lx are the Lamé coefficients:

kx ¼Extxy

ð1þ txyÞð1� 2txyÞ

lx ¼ Gxy ð17Þ

By means of destructive procedures, the mechanical descriptorsthat define the compliance tensor from Eq. (8) were determined.These data are for non-immersed GFRP specimens presented inTable 3 as an average value of five samples from the same product.Menard [36] has shown that the glass-transition temperature andthe Arrhenius activation energy of this transition can bedetermined.

Ez, txz and Gxz were determined from measurements of thepropagation speed of the ultrasound along the direction Z (accord-ing to Fig. 9); the other mechanical properties being determinedfrom the propagation speed of the Lamb waves, the fundamentalmodes S0 and A0.

Fig. 10a presents the signal received by the reception transducerduring the examination of the 7201 composite, where the modesA0, S0 and S1 can be distinguished. For a more reliable identifica-tion, the amplitude spectrum was traced and is presented inFig. 10b. Fig. 10c presents the corresponding spectrogram. The sig-nal is presented in the time-domain (Fig. 10a), the frequencydomain (Fig. 10b) and as a spectrogram (Fig. 10c).

Using the spectrum-phase method, the phase velocity of A0 andS0 were determined, and, using Eqs. (14) and (15), the other mea-sures from the compliance tensor from Eq. (8) can be determined.The data from the ultrasound measurements for all three types ofcomposite are collected in Table 4.

Comparing the data from Tables 3 and 4, it is clear that there is avery good correlation between the mechanical measures thatdefine the compliance tensor, which is determined by the destruc-tive and non-destructive procedures.

4. Conclusions

The water-absorption behaviors of three types of GFRP compos-ite were recorded, and from these results we can conclude thefollowing:

– The destructive tests showed good mechanical results for thecomposite 7524, where the polyester is produced in-situ. In-situproduction means a cheaper process in comparison with thesimilar composite 7201. The glass-transition temperature is10 �C higher in the case of the 7524 composite, compared tothe 7201 composite.

– For a more effective use of the composite materials, the princi-pal mechanical parameters, such as the compliance tensor,must be known. This can be obtained from destructive testsor by means of nondestructive tests using ultrasound.

– The measurement of the propagation speed of the longitudinaland transversal waves can be used with good results for thedetermination of the elastic modulus Ez, the shear modulusGxz and the Poisson’s ratio txz.

– For the determination of the elastic modulus Ex, the shear mod-ulus Gxy and the Poisson’s ratio txy, the use of Lamb waves isrequired, the phase velocity of fundamental modes beingdirectly connected to the mechanical parameters.

– A method for the generation and reception of Lamb waves inplates of composite materials involves the use of air-coupling,low-frequency, ultrasound transducers in a pitch–catchconfiguration.

16 R. Šturm et al. / Composites: Part B 71 (2015) 10–16

– The results of the nondestructive measurements described inthis paper are in good agreement with those obtained usingclassical destructive tests.

Acknowledgements

This paper is partially supported by The National Authority forScientific Research of Romania (ANCS) as part of the Romanian–Slovenian Bilateral Cooperation Program-Contract No. 371/2009 –RO-SI and Slovenian Research Agency for the Republic of Slovenia(SRA) under Romanian Slovenian Bilateral Cooperation Program-Contract No.: BI-RO/10-11-002.

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